We introduce an open-source library for machine-checked control theory in the interactive proof assistant Lean to lay foundations for the verification of cyber-physical systems. To this end, as representative theorems, we present formalizations of Lyapunov stability theory and the small-gain theorem. First, the machinery employed for formalizing Lyapunov stability, i.e., neighborhood filters, allows stating a Lyapunov theorem that covers both points and sets and applies to continuous, discrete, and hybrid systems. Second, the small-gain theorem is proved via stating input-output systems as relations without the usual well-posedness assumption. The Lean formalization of each of these theorems is then presented. We conclude by discussing the library architecture and mentioning some of the other system theoretic results that are formalized in the library along with future plans.
We present Ripple, an open, AI-formalized Lean 4 framework for the mathematics of computing with chemical reaction networks (CRNs) -- one extensible, machine-checked development that gathers several strands of the field into a single setting, and is built to grow. It formalizes:…
We disprove the conjecture that every globally asymptotically stable homogeneous polynomial vector field admits a homogeneous polynomial Lyapunov function. The counterexample is a planar homogeneous cubic polynomial vector field with integer coefficients. It admits no positive de…
This article develops a large-signal stability analysis for a sampled-data optimization-based secondary controller for distributed energy resources (DERs) in power systems. The induced closed loop combines nonlinear inverter power-flow dynamics, filtered active and reactive power…
This paper presents a method for computing inner polytopic approximations of admissible sets for continuous-time linear control systems subject to affine state constraints. Building upon barrier theory and the explicit solution of linear systems, a structured sampling procedure i…
We consider the uniform exponential stability analysis of infinite-dimensional impulsive systems defined on a Banach or Hilbert space, whose flow is governed by a fixed $C_0$-semigroup generator and whose jumps occur at a prescribed time sequence. While the flow and jump maps are…
This paper illustrates the Pick-to-Learn methodology applied to the calibration of a Model Predictive Control policy. While developed around a specific example, the presentation is meant to highlight a methodology of broad applicability. The example concerns an aircraft traveling…